Discrete approximations of differential inclusions. The idea of our proof is to apply the results of [1]} on the stochastic approximation of differential inclusions to our setting. To this end, we consider an \(\mathbb {R}^d\) -valued sequence \((y_k)\)  constructed as follows:
\(y_{k+1} = y_k - \gamma _k \nabla \ell (y_k) + \gamma _k \eta _{k+1} - \gamma _k u_k \, ,\) 
